A Stochastic Gradient Descent (SGD)-based Latent Factor Analysis (LFA) model is highly efficient in representative learning on a High-Dimensional and Sparse (HiDS) matrix, where the learning rate adaptation is vital in its efficiency and practicability. The learning rate adaptation of an SGD-based LFA model can be achieved efficiently by learning rate evolution with an evolutionary computing algorithm. However, a resultant model commonly suffers from twofold premature convergence issues, i.e., a) the premature convergence of the learning rate swarm relying on an evolution algorithm, and b) the premature convergence of an LFA model relying on the compound effects of evolution-based learning rate adaptation and adopted optimization algorithm. Aiming at addressed such issues, this work proposes an Hierarchical Particle swarm optimization-incorporated Latent factor analysis (HPL) model with a two-layered structure. The first layer pre-trains desired latent factors with a position-transitional particle swarm optimization-based LFA model with learning rate adaptation; while the second layer performs latent factor refinement with a newly-proposed mini-batch particle swarm optimization algorithm. Experimental results on four HiDS matrices generated by industrial applications demonstrate that an HPL model can well handle the mentioned premature convergence issues, thereby achieving highly-accurate representation to HiDS matrices.

Concept Factorization (CF) models have attracted widespread attention due to their excellent performance in data clustering. In recent years, many variant models based on CF have achieved great success in clustering by taking into account the internal geometric manifold structure of the dataset and using graph regularization techniques. However, their clustering performance depends greatly on the construction of the initial graph structure. In order to enable adaptive learning of the graph structure of the data, we propose a Concept Factorization Based on Self-Representation and Adaptive Graph Structure Learning (CFSRAG) Model. CFSRAG learns the affinity relationship between data through a self-representation method, and uses the learned affinity matrix to implement dynamic graph regularization constraints, thereby ensuring dynamic learning of the internal geometric structure of the data. Finally, we give the CFSRAG update rule and convergence analysis, and conduct comparative experiments on four real datasets. The results show that our model outperforms other state-of-the-art models.

High-Dimensional and Incomplete matrices, which usually contain a large amount of valuable latent information, can be well represented by a Latent Factor Analysis model. The performance of an LFA model heavily rely on its optimization process. Thereby, some prior studies employ the Particle Swarm Optimization to enhance an LFA model's optimization process. However, the particles within the swarm follow the static evolution paths and only share the global best information, which limits the particles' searching area to cause sub-optimum issue. To address this issue, this paper proposes a Dynamic-neighbor-cooperated Hierarchical PSO-enhanced LFA model with two-fold main ideas. First is the neighbor-cooperated strategy, which enhances the randomly chosen neighbor's velocity for particles' evolution. Second is the dynamic hyper-parameter tunning. Extensive experiments on two benchmark datasets are conducted to evaluate the proposed DHPL model. The results substantiate that DHPL achieves a higher accuracy without hyper-parameters tunning than the existing PSO-incorporated LFA models in representing an HDI matrix.

A recommender system (RS) aims to provide users with personalized item recommendations, enhancing their overall experience. Traditional RSs collect and process all user data on a central server. However, this centralized approach raises significant privacy concerns, as it increases the risk of data breaches and privacy leakages, which are becoming increasingly unacceptable to privacy-sensitive users. To address these privacy challenges, federated learning has been integrated into RSs, ensuring that user data remains secure. In centralized RSs, the issue of rating bias is effectively addressed by jointly analyzing all users' raw interaction data. However, this becomes a significant challenge in federated RSs, as raw data is no longer accessible due to privacy-preserving constraints. To overcome this problem, we propose a Federated Bias-Aware Latent Factor (FBALF) model. In FBALF, training bias is explicitly incorporated into every local model's loss function, allowing for the effective elimination of rating bias without compromising data privacy. Extensive experiments conducted on three real-world datasets demonstrate that FBALF achieves significantly higher recommendation accuracy compared to other state-of-the-art federated RSs.

Knowledge is hidden in massive high-dimensional and incomplete (HDI) data generated by modern intelligent applications, but missing attributes and relations make it difficult to acquire this knowledge directly. Latent feature learning (LFL) addresses this problem by mapping related entities into a low-dimensional space, constructing an approximation model from known values, and estimating missing relationships through iterative optimization. However, its single-path optimization may converge prematurely near a suboptimal solution. Incorporating swarm intelligence (SW) into LFL introduces parallel evolution and group collaboration, thereby providing multiple search paths for latent knowledge refinement. This chapter introduces three classical SW-incorporated LFL methods – particle swarm optimization (PSO), differential evolution (DE), and beetle antennae search (BAS) – and compares their search mechanisms, knowledge-acquisition accuracy, exploration ability, and computational efficiency. In the considered framework, an SGD- or position-transitional latent factor analysis (PLFA)-based LFL model first performs the initial optimization, after which the SW layer refines learning rates or latent factors. The PSO coordinates particles through personal and social experience; DE generates candidates through differential mutation, crossover, and selection; and BAS searches promising directions through paired antennae with Adam-based step-size adaptation. The synthesized results indicate that all three methods improve LFL-based knowledge acquisition, while exhibiting different strengths: PSO offers a hierarchical bridge between latent feature and swarm spaces, DE provides strong population diversity and competitive accuracy, and Adam-adjusted BAS achieves focused local refinement with few outer iterations.